$\iota$ 1584 2008 8-20 8 1 (Kiyoto Kawai), (Kazuyuki Sekitani) Systems engineering, Shizuoka University 3 10, $2N6$ $2m7$,, 53 [1, 2, 3, 4] [9, 10, 11, 12], [8] [6],, ( ) ( ), $\ovalbox{\tt\small REJECT}\backslash ^{9}$, 2006 \not\subset 12,, Data Envelopment $Analy_{8}is$ (DEA) [13] 12 Bradley-Terry(BT) [$\eta$, $Aa$, DEA,, $2m7$ 1, [5] DEA 2 BT 21,, 12 2006,,,, 1, 269 258,, 3,,, 1 1 1, 1,,
9 1: 12 2006 $O$,,, ( ), BT $2W6$ 22,, BT [7] BT, 12, $\xi_{1}=$ $(x_{11}, x_{12}, \ldots,x_{112}),$ $\xi_{2}=(x_{21}, x_{22}, \ldots, x_{212})$ $i$ $j$ j, $i$ $j$ $q_{1j}$ $p_{ij}= \frac{x_{2i}}{x_{2i}+x_{1j}},q_{lj}=\frac{x_{1i}}{x_{2j}+x_{1i}}$ $(i\neq j)$ (1),, ( ), $i$ $j$,,, ( ) $r_{\{j}$, $i$ $j$ $8_{ij(=r4_{J^{-r_{ji})}}}$ 2006 2 12 $(r:j, s_{*j})$ 2 2 579, 579, 2 293, 293 2 /, $B$ ) $-$
$\epsilon_{1}$ $r_{1\dot{f}}$ $\backslash$ 10 $\varpi$ 2: $2006$ : $\vdash$ 12 $\ovalbox{\tt\small REJECT} S$ $\ovalbox{\tt\small REJECT}_{J\backslash I}$ $\ovalbox{\tt\small REJECT}_{\text{ }\backslash \mathfrak{l}}$ $(s_{ji})$ : : $\ovalbox{\tt\small REJECT}\backslash$ $/c$ $1$ ) $-\cdot-(t_{lj})$ $\frac{\text{ }}{\text{ }*\text{ }05795765805865791661621154160153}$ $\neg$ $\cdot t-\cdot-$ $02932672722802857472556887$ 5570 681678552555158163151149156153 2250 307233278303755175608086 6925770 $5605535\infty$ 154157162153160159 $u82440$ 2602512797387 SO 848584 5685736760 555569161149146156155149 2342382650 218277706856647070 5855385525550 571161152154157151160 $2762472u$2370 248645960646583 $5605u5825665780$ 150148150153151152 2472402582432480 7771 7361 6779 1641621521651461520 508525501521522 686063897267 204216242265264 164164150150154154521 533538526517 73786465 7082 2600 267275265272 1521501591511521575266150 510541534 607579697881 1782700 226258257 1541421521631611585025315090 522525 606487798358 2362242060 216280 1441511551491481555105245225140 504 536677536575 2262682052180 253 $*$ 1571681671561591586175235295145170 $*$ $\ovalbox{\tt\small REJECT}$ $7177697378762362402192362u0\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}$ $r\iota j$ 2 (2) $tf$ $P:j$ $Pr(r_{tj})=(\begin{array}{l}n_{ij}r_{tj}\end{array})p_{1j }r(1-p_{lj})^{n}u-r_{j}$ (2), $\{r_{lj}\}$ (1) 1 $\sum_{\iota\approx 1}^{12}\sum_{j\prime i}^{12}\frac{(r_{jj}-n_{1j_{\overline{\alpha_{1}}+oe_{1f}}^{x_{aarrow)^{2}}}}}{n_{i\dot{g}}\frac{l}{x_{ll}}aarrow}+\frac{(\epsilon_{ji}-n_{j:}}{n_{j1}\frac{x_{13}}{xa+ae\iota g}}$ (3) (3) $\xi_{2}$ (3) $ij$, (3),, $x_{1},x_{2}$ $x_{11}=x_{12}=\cdots=x_{112}=x_{1}$, $H_{0}$ : (4) $x_{21}=x_{22}=\cdots=x_{212}=x_{2}$, $H0$, $\xi_{1}=x_{1},\xi_{2}=x_{2}$ (3), $x_{1},x_{2}$ $H_{0}$, $x_{1},$ $x_{2}$ $x_{1}$ (4) $x_{2}$ $( \sum_{1=1}^{12}\sum_{j\neq i}^{12}\frac{r_{i\dot{g}}^{2}}{n_{1j}})\frac{x_{1}}{x_{2}}+(\sum_{i=1}^{12}\sum_{j\neq i}^{1l}\frac{\epsilon_{j1}^{2}}{n_{1j}})\frac{x_{2}}{x_{1}}$ (5)
$\frac{\sum_{\dot{g}\neq i}n_{1j_{\varpi_{1f}+\overline{x_{2}}}^{arrow x}}}{\sum_{j\neq:}n_{1j}}$ 11 (5) 2 $A=[ \sum_{t=1}^{12}\sum_{j\neq:_{n}}^{12_{\lrcorner_{\frac{i}{f}}}^{2}}^{0}$ $\sum_{1=1}^{12_{\sum_{0}}12_{a}^{r^{l}}}j\neq i\mathfrak{n}\ell d]$ $i$, A (, $a_{1j}$, (5) $i$ $[a_{1j}x_{j}^{*}/x:]$ $i$ (6) $( \sum_{-1}^{12}\sum_{j\neq i}^{12}\frac{r_{j}^{2}}{m_{j}})\frac{x_{1}^{*}}{x_{2}}=(\sum_{i-1}^{12}\sum_{jl}^{12}\frac{\epsilon_{j}^{2}}{n_{j}})\frac{xi}{xi}$ (6) 2 (6) $x_{1}^{*}=5709$, $x_{2}^{l}=2624$, (3) $=172473$ (7) $131(=12-(2-1))$, (3) 131 $H_{0}$ 5% 158712, $H_{0}$, 131 1% 171567, 1%,, 23 BT 12 $\epsilon_{1},\epsilon_{2}$ (2) $L$ $L$ $L= \prod_{t\approx 1}^{12}\prod_{i\prime j}(\begin{array}{l}n_{ij}r_{ij}\end{array})(\frac{1}{x_{2i}+x_{1j}})^{n_{j}}\prod_{\iota=1}^{12}x_{2l}^{u_{l}}\prod_{k=1}^{12}x_{1k}^{v_{k}}$ (8) $l$, $u\iota vk$,, $k$ $u_{l}=\sum_{j\neq l}r_{lj},$ $v_{k}= \sum_{j\neq k}s_{jk}$ $L$ $\xi_{1},\xi_{2}$ BT [7] 2 12 $\xi_{1}$ $\xi_{2}$ 3,, $i$ $(\xi_{1}, \xi_{2})$, $\epsilon_{1},\epsilon_{2}$ BT,, 3 BT 112181 f $109(=12x11-(24-1))$ 109 5% 134369, 2 BT, 109 10% 128298, 10% 3, 1 4
$ $ 4 $ $ 4 12 3: 12 2006 \mp, $(x_{1})$ $(x_{2})$ $(x_{1})$ $(x_{2})$ 6202 2718 5883 2589 5799 2710 5720 2846 $27\mathfrak{X}$ 5604 6058 25% 5916 246$ 5837 2557 5686 2524 5$4u$ 2$6m$ 6360 2537 5111 2634 4:,, $(x_{1})$ $(x_{2})$ 1 2 3 5 6 1 2 3 5 6 )1 4,,,,, 2 2,,, 4 3,, 4, 2 4, 4 2, 2, 2, 2, 2,, 1, 2,, 2 4 1, 1 3 12, 1
$\gamma$ $\gamma$ 13 (05), 2, 2 3 1 1 1, $2W6$, 12, 3 1,, 2,,,, DEA, DEA, ( ), ( ),, DEA DEA, 1, 1,, $\gamma$,, $k$ $x_{1k}$, $x_{2k}$, $2N6$ $y_{k}$ $k$ $x_{k}$ $(x_{1k}, x_{2k})$ $\gamma$, $P(\gamma)$ (9) $P(\gamma)\equiv\{(x,y) j\approx 1j\approx 11212\}$ (9) (9), (, )
14?, (10) $k$ max $\{\phi y_{k} (x_{k},\phi y_{k})\in P(\gamma)\}$ (10) $k$ $\phi^{*}$ (10) (10), $1/\phi^{*}$ DEA, $1/\phi^{*}$ $k$ $P(\gamma)$ $\gamma$, 6 5, $\gamma=630$, $\gamma=664$ 6; 5 2002 623 647 2003 A 599 2004 685 597 2005 617 $2\alpha)6$ $617614$ $1/\phi^{*}$ 5, (1), (1), (987), (979), (948), (842), (808), (786) (754), (736), (6%), (667), 5 6 01 5,,, 1, 1, 2, 35 2 3 145 $-$ $622603$
$\gamma$ 15 3 1, 3, 5 ( ), 5, $\gamma=630$ 664, 633, 975,,,, 5 1, $k$ $\{j \phi^{*}y_{k}=\sum_{=\dot{f}1}^{12}y_{j}\lambda_{j},$ $oe_{k} \geq\sum_{j=1}^{12}x_{j}\lambda_{j},$ $\lambda_{j}>0\}$ (11), 10,, ( ),, 605 603, 1, $ \supset$, 617, 5 5 206,,, 5 $2\infty 6$ 5, 6,,,? (10) $\phi$, $k$ $\max\{d_{1}+d_{2} (x_{k}-d, \phi^{*}y_{k})\in P(\gamma)\}$ (12), $d$ $(d_{1}, d_{2})$ $k$ (12),,, (12) $d_{1}+h$ $d_{1}$ $d_{2}$ (12) 7, 5 4,,,, $\{\lambda(0363, W39)+(1-\lambda)(0378,0) 0\leq\lambda\leq 1\}$,,, $\gamma=630$ 5 $\gamma=630$, 7 7 (,,,,,, ), 1 DEA 2 2006 2 1
16 7; $m\alpha d_{1}+2$ $ 003639$ $\text{ _{}0}\text{ _{}9}\max$ $\frac{m\alpha d_{2}}{\text{ }}0378$ 3181 3181 1599 1599 0267 0267 $009080090800\ovalbox{\tt\small REJECT}$ 4 41,,, 2007 $P(\gamma)$, 2007 $\alpha_{g}$, $\alpha_{g}$ $\alpha_{g}$, $d=$ $d_{l}$ (, [ ), $d=(d_{1}, d_{2})$, 2006 $x_{g}=(x_{1g}, x_{2g})$, $x_{g}+d=(x_{1g}+d_{1}, x_{2g}+d_{2})$ $P(\gamma)$, $x_{g}+d$ $\alpha_{g}$ $(x_{g}+d, \alpha_{g})\in P(\gamma)$,, $d$ $\beta\in[0, \infty$ ) (13) nin $\{d_{1}+\beta d_{2} (x_{g}+d,\alpha_{g})\in P(\gamma)\}$ (13) $\beta$ ( ) $\beta>1$, $\beta<1$, $ \beta-1 $, $y=\alpha_{g}$ $P(\gamma)$ 2 2, $\alpha_{g}$ 206 $(x_{h},y_{h})$ $y=\alpha_{g}$ $P(\gamma)$ 2, 1 $(x_{h}, y_{h})$ $y=\alpha_{g}$ $\alpha_{g}/y_{h}(x_{h}, y_{h})$ $x$ $\alpha_{g}/y_{h}x_{h}$, $(x_{s},ys)$, $y=\alpha_{g}$ $P(\gamma)$ $\alpha_{g}/y_{s}(x_{9},ys)$, $a_{g}/y_{s}x_{s}$ 6, 5 614, $\alpha_{g}=0614$ (13) $f$, $\beta^{*}=03686$ $\beta\in[0, \beta^{t}$ ), $x_{g}+d^{*}$, $\beta\in[0,\beta^{*}$ ), $d_{1}^{*}<0,$ $d_{2}^{l}>0$, $x_{1g}$ $x_{2g}$ $\alpha_{g}$
17 2: $y=a_{k}$ $P(\gamma)$, $\beta=\beta^{*}$ $XQ+X$ $\beta=\beta^{*}$, $x_{1g}$ $X2G$,, $\beta>\beta$, $x_{g}+d^{*}$, $\beta>\beta^{*}$, $d_{1}^{*}>0$ $d_{2}^{*}>0$,, $\alpha_{g}$, $(\beta)$ $\alpha_{g}=0614$ $\beta$, $\alpha c=0614$,, ( ) ( ), $\beta\in[0, \beta^{*}]$,,, $\alpha_{g}=0614$, $a_{g}=0614$, $a_{g}$, $a_{g}$ $\frac{a_{g}}{0597}x572\geq 5915$ (14) (14) $a_{g}\geq 06174$, 6174,, 42 2\omega 07, 8 2006 7 $2W7$ 4 2006 8 9, MLB 4 2006 2006,,,, 8 12 2006 9 9 5
$\text{ ^{}1}J\text{ ^{}t}j$ 18 8: 06-07 / / $\overline{k}lhffi$ $t$ ) y t $\wedge$ $71s/\backslash \backslash$, $\aleph$ $\aleph$ NUt $*$ $M\overline{LB}ff$ $MLBMLBp$ $/p$ } $1$ $i$ } l \Re $i$ $6$ $f_{\overline{fl\xi@\re r_{ij}*\backslash f\mathfrak{w}\re \text{ }}}$ $/\backslash ( ) 4g\acute $\backslash \not\in n\neq$ 9: 2\alpha \cdot$ $\ovalbox{\tt\small REJECT}_{\text{ }}\overline{\text{ }}$ $\ovalbox{\tt\small REJECT}$ $)$ $\sim$ 232026242526617158700 5 4 9 5 101018251421027 68 $T $ 8 9 9 9 12120 2742293835 $) $\ovalbox{\tt\small \epsilon_{1j}\frac{\ovalbox{\tt\small REJECT} \text{ }}{\text{ }*\cdot\dagger REJECT}_{\text{ }}($ j-7/\backslash \cdot 1j-r}$ $\ovalbox{\tt\small REJECT}$ 2725252526250 8587798887 $\ovalbox{\tt\small 109799149200 23290 REJECT} 6 $26P$ 15512713968500 31510 6 10 6 15119 9 14 20210 263529 2 1 1 ( ) 10181811 1421 32350 354945 $7^{ffl\Re)}$ 129 8 6 3 3 3 2 120 4 7 4 1915200 8 26 7 3 3 3 5 2 ( ) 180 5 8 6 1 2 4 2 1 2 1 $\varpi\backslash ffi\re$ ) 2 6 4 108 2 3 3 6 5 3 $\ovalbox{\tt\small REJECT}$ ( ) 5268 b40 4752261612118 8 1635220 280 230 408 32 4 3 7 3 1 7 1 3 2 4 ( ) 3351260 430 290 569 48 ( ) 2212220 9 12167 133 1110 150 200 1 1 ( ) 240 310 ( ) 3 3 1 5 1 2 120 3 113 1 6 $30$ $31$ $00$ $40$ $00$ $00$ $31$ $00$ $03$ $00$ $22$ $\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}((*l$ ) $01$ ) (\approx 1 3 &*) ( 200&07 23, 23 5 109 155, 155, 109 2006, 9 2, 5, 23, 5, 18, 5, 18, 5, 18, 2 9, 2 9,,,,,
19, 2, MLB $G=(\overline{x}_{1G},\overline{x}_{2G})$ 9 2 $(\overline{x}_{1g},\overline{x}_{2g})=(5923,2642)$ (15) 0$W8$, 0149, 2006 12 6, $\overline{x}_{g}$, 1 630, $\gamma=630$ (16) max (16) $\{a (\overline{x}_{g},a)\in P(\gamma)\}$ (16) 3 10 10 608 617, 5 0614, 2006 2 592 10: 608, $0973(=$ 0592/0608), 592 5, ( B,,, ) 0948, 0948 576 576 2006 3 573 2004, 3, $2W7$, $2m7$ e 3 0973 $2W6$ 2, 0948 $2\infty 6$ 3,,, 5 $/\backslash 2006 ^{l}$ ( 2) 12,, (9) 5 1 2006, ( 1 7) 2 2006, ( 5)
20 3 2006,,,,,, ( 5) 4 2007 ( 2) 6 2006 2007 $\cdot$ ( 6, 10), 2007 * ( 5, 10) 1,, DEA, 2,,,, (C) No 18510121 [1], : : (HBJ, 1988) [2] : \sim (, 2000) [3] : (,2006) [4], : (, 1989) [5],,, (2006) 12/07, 157-168 [6], :,, 537 (205) 23-25 $\eta$ [ : 5, (, 1991) [8] :,, 49 (2004) 380-389 [9], : $DEA/OERA$, 7 (1997) pp41-51 [10] :, 38 (1987) 689-697 [11] :, 47 $(2W2)137-141$ [12] : $DEA$ [13] :, (, 1993), 38 (1993) 146-153